In this paper we propose a new speech compression technique employing psychoacoustic model and a general approach for Filter Bank Design using optimization. This technique is inspired from an audio compression technique using psychoacoustic model and a Modified Discrete Cosine Transform (MDCT) filter banks of 32 filters. In fact, in this proposed approach, we have used Uniform/Non-Uniform Filter Bank (which is designed using optimization) instead of a MDCT filter banks of 32 filters. The two techniques are evaluated and compared with each other by computing bits before and after compression. They are tested and applied to different speech signals. The simulation results obtained from the computation of the compressed files size and the Compression Ratios (CR), show that the proposed technique outperforms the second one. In term of perceptual speech quality, the outputs speech signals of the proposed compression system are with good quality. This is justified by the computation of SNR (Signal to Noise Ratio), PSNR (Peak Signal to Noise Ratio), NRMSE (Normalized Root Mean Square Error) and PESQ (Perceptual evaluation of speech quality). We have also compared the proposed technique to one previous research work which is a speech compression technique based on Discrete Wavelet Transform (DWT) and integrating a Voice Activity Detection (VAD) Module. This comparison is also based on the computation of SNR, PSNR, NRMSE, PESQ and CR and the obtained results show that the proposed technique outperforms this third technique based on DWT and VAD.